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Angles inscribed in the same arc are...

Angles inscribed in the same arc are

A

congruent

B

complementary

C

supplementary

D

none of these

Text Solution

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The correct Answer is:
A
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Corollaries of inscribed angle theorem : Angle inscribed in the same arc arc contruent Given : (1) A circle with centre O (2) /_ABD and /_ACD are inscribed in arc ABC and intercepts arc APD. To prove : /_ABD ~= /_ACD

Prove that, angles inscribed in the same are arc congruent.

Knowledge Check

  • Find the ratio of the areas of squares circumscribed about and inscribed in the same circle.

    A
    `1:3`
    B
    `2:1`
    C
    `sqrt(2) :1`
    D
    `1:sqrt(2)`

  • If an equilateral triangle ABC is inscribed in a circle with centre O then the measure of angle AOB is

    A
    ` 60 ^(@) `
    B
    ` 90 ^(@)`
    C
    ` 120 ^(@) `
    D
    ` 180^(@) `

  • ABC is an equilateral triangle inscribed in a circle. D is any point on the arc BC. What is angleADB equal to?

    A
    `90^@`
    B
    `60^@`
    C
    `45^@`
    D
    None of these

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    Show that any angle in a semi-circle is a right angle. The following arc the steps involved in showing the above result. Arrange them in sequential order. A) therefore angleACB=180^(@)/2=90^(@) B) The angle subtended by an arc at the center is double of the angle subtended by the same arc at any point on the remaining part of the circle. c) Let AB be a diameter of a circle with center D and C be any point on the circle. Join AC and BC. D) therefore angleAD = 2 xx angleACB 180^(@)=2angleACB(therefore angleADB=180^(@))

    Prove that an angle inscribed in a semi-circle is a right angle using vector method.

    If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then prove that PA is angle bisector of angleBPC .

    A triangle is inscribed in a circle.The vertices of the triangle divide the circle into three arcs of length 3,4 and 5 units.Then area of the triangleis equal to:

    An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. What is angleBDC equal to?

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